Normally in a cycled tank you will see a reading of Nitrate, since it is the end-product of the bacteria converting the fish's waste.
I think it is possible to have such minute amount of nitrates in your tank that the reading may come back as 0 if you have a very small bioload (just one Betta) and a large amount of water while doing large weekly water changes.
It is also possible that your test kit is faulty or that the chemicals in the test kit bottles aren't mixed together well enough. You have to shake those bottles to the point that your arm nearly falls off, shake it really well, to mix in the two layers in the bottle each time you are doing a test. You could also bring a sample of your tank water to your LFS and ask them if they could do a test for you, ask them to give you the numbers of the reading, not just a verbal confirmation that 'the water is fine'!
A quick question: did you do a fish-in-cycle?